On the Asymptotic Properties of Hogg's Q Statistic

1986 ◽  
Vol 35 (1-2) ◽  
pp. 77-84 ◽  
Author(s):  
H.N. Nagaraja
Keyword(s):  
Order Statistics ◽  
Limit Distribution ◽  
Asymptotic Theory ◽  
Asymptotic Properties ◽  
Linear Functions ◽  
Close Approximation ◽  
Optimum Proportion ◽  
Sample Data ◽  
Q Statistic ◽  
Family Of Distributions

The asymptotic properties of Qn, a measure of tail thickness introduced by Hogg, are investigated. The nondegenerate limit distribution of Qn is obtained as an application of a bivariate extension of a result on smooth linear functions of order statistics, due to Stigler. The limiting result is helpful in indicating the optimum proportion of the sample data to be used in the construction of Qn for discriminating between members of a symmetric family of distributions. The asymptotic theory is also used to find a close approximation to the expected value of Qn. This approximation works well for moderate sample sizes for distributions in the symmetric family.

Asymptotic Properties of Linear Functions of Order Statistics for Non­Stationary Mixing Processes

1979 ◽  
Vol 28 (1-4) ◽  
pp. 19-36
Author(s):  
David A. Sotres ◽  
Malay Ghosh
Keyword(s):  
Order Statistics ◽  
Asymptotic Properties ◽  
Random Variables ◽  
Linear Functions ◽  
Mixing Processes

For ø­mixing sequences of random variables, under certain conditions, we provide a representation of linear functions of order statistics as sample means pius remainder terms. The remainder terms are shown to converge to zero almost surely at certain rates.

scholarly journals On stochastic comparisons of maximum order statistics from the location-scale family of distributions

2017 ◽  
Vol 160 ◽  
pp. 31-41 ◽  
Author(s):  
Nil Kamal Hazra ◽  
Mithu Rani Kuiti ◽  
Maxim Finkelstein ◽  
Asok K. Nanda
Keyword(s):  
Order Statistics ◽  
Stochastic Comparisons ◽  
Maximum Order ◽  
Scale Family ◽  
Family Of Distributions

A clustering law for some discrete order statistics

2003 ◽  
Vol 40 (01) ◽  
pp. 226-241 ◽  
Author(s):  
Sunder Sethuraman
Keyword(s):  
Distribution Function ◽  
Positive Integer ◽  
Order Statistics ◽  
Law Of Large Numbers ◽  
Asymptotic Properties ◽  
Random Variables ◽  
Large Numbers ◽  
The Law ◽  
Sample Maximum ◽  
Independent Identically Distributed

Let X 1, X 2, …, X n be a sequence of independent, identically distributed positive integer random variables with distribution function F. Anderson (1970) proved a variant of the law of large numbers by showing that the sample maximum moves asymptotically on two values if and only if F satisfies a ‘clustering’ condition, In this article, we generalize Anderson's result and show that it is robust by proving that, for any r ≥ 0, the sample maximum and other extremes asymptotically cluster on r + 2 values if and only if Together with previous work which considered other asymptotic properties of these sample extremes, a more detailed asymptotic clustering structure for discrete order statistics is presented.

A point-process approach to almost-sure behaviour of record values and order statistics

1996 ◽  
Vol 28 (02) ◽  
pp. 426-462 ◽  
Author(s):  
Charles M. Goldie ◽  
Ross A. Maller
Keyword(s):  
Order Statistics ◽  
Point Process ◽  
Relative Stability ◽  
Asymptotic Properties ◽  
Random Variables ◽  
Record Values ◽  
Process Approach ◽  
Integral Conditions ◽  
Comprehensive Investigation ◽  
Trimmed Sums

Point-process and other techniques are used to make a comprehensive investigation of the almost-sure behaviour of partial maxima(the rth largest among a sample ofni.i.d. random variables), partial record valuesand differences and quotients involving them. In particular, we obtain characterizations of such asymptotic properties asa.s. for some finite constantc, ora.s. for some constantcin [0,∞], which tell us, in various ways, how quickly the sequences increase. These characterizations take the form of integral conditions on the tail ofF,which furthermore characterize such properties as stability and relative stability of the sequence of maxima. We also develop their relation to the large-sample behaviour of trimmed sums, and discuss some statistical applications.

scholarly journals ASYMPTOTIC THEORY FOR NONLINEAR QUANTILE REGRESSION UNDER WEAK DEPENDENCE

2015 ◽  
Vol 32 (3) ◽  
pp. 686-713 ◽  
Author(s):  
Walter Oberhofer ◽  
Harry Haupt
Keyword(s):  
Quantile Regression ◽  
Asymptotic Normality ◽  
Regression Model ◽  
Asymptotic Theory ◽  
Asymptotic Properties ◽  
Covariance Estimation ◽  
First Order ◽  
Regression Quantiles ◽  
Quantile Regression Model ◽  
Consistency And Asymptotic Normality

This paper studies the asymptotic properties of the nonlinear quantile regression model under general assumptions on the error process, which is allowed to be heterogeneous and mixing. We derive the consistency and asymptotic normality of regression quantiles under mild assumptions. First-order asymptotic theory is completed by a discussion of consistent covariance estimation.

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